The Prime Minister will meet newspaper editors next week, to discuss the future of press regulation and whether the industry can deliver it alone.

It comes as an online petition demanding the Government act on Lord Justice Leveson's recommendations in full has attracted more than 80,000 supporters in less than 24 hours.

Support for the petition launched by Hacked Off, the group campaigning for victims of phone hacking, has doubled overnight.

The Culture Secretary has warned newspaper editors not to drag their feet in acting on Lord Justice Leveson's calls for setting up a new press watchdog.

Maria Miller, joined by David Cameron, will meet the newspaper industry's most powerful editors next week to push for urgent action.

Paul Dacre has acknowledged that swift action is needed

Downing Street said the PM will call for a timetable to be set for creating a new independent press watchdog.

Lord Hunt of Wirral, the chairman of the Press Complaints Commission, who will also attend, told The Times he wanted a speedy industry resolution to help persuade the public and MPs that laws were not needed to underpin the new independent regulator.

"There's an awful lot we can agree on and I have suggested to the industry (that we) all read the report, digest it and seek out the common ground and unite with one voice," he said.

Ms Miller's warning will come the day before editors on the Code of Practice Committee, chaired by Daily Mail editor Paul Dacre, meet to decide how to tackle the Leveson recommendations.

Mr Dacre said: "Lord Justice Leveson has set us a number of challenges: our task is to address them as urgently as possible."

It comes as reports emerged that Foreign Secretary William Hague warned Cabinet colleagues earlier this week that a "Leveson law" would undermine the UK's ability to address freedom of speech issues globally, particularly on cases such as the jailing of punk band Pussy Riot in Russia.

A Government source told The Daily Telegraph: "It was a very serious presentation. He warned that Britain demonstrating that we have a free press is part of our ability to say we believe in democracy."

But David Cameron is under intense pressure to drop his opposition to a law backing up the new watchdog the press has been tasked with devising.

The Prime Minister is facing a backlash from victims of media intrusion over his resistance to legislation.

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Gallery: Leveson Inquiry Report Recommendations

The new body would be made up of all the newspapers that chose to sign up.

Author JK Rowling has said that she felt "duped and angry" by Mr Cameron's hesitance to "cross the Rubicon" and introduce a press law.

The Harry Potter author, who gave evidence about press intrusion into her family's privacy to the inquiry, said: "If the Prime Minister did not wish to change the regulatory system even to the moderate, balanced and proportionate extent proposed by Lord Leveson, I am at a loss to understand why so much public money has been spent and why so many people have been asked to relive extremely painful episodes on the stand in front of millions."

The most high-profile victims of phone hacking refused to meet the Culture Secretary on Friday, saying they felt let down by Mr Cameron's response.

Despite the boycott, Ms Miller has met the leaders of the Hacked Off campaign and described the talks as frank.

Madeleine McCann's father Gerry said giving evidence to the Leveson Inquiry would have been "almost useless" if the proposals were not implemented in full, and urged the Prime Minister to "do the right thing".

London bombing hero Paul Dadge, a victim of phone hacking, said he was very disappointed with Mr Cameron's stance and called on him to back the public rather than the press.

Christopher Jefferies, the landlord wrongly arrested for the murder of Joanna Yeates, warned it would be a "disaster" if the recommendation on legislation was ignored, and said he would feel "let down" by Mr Cameron.

Video:Leveson: Gerry McCann Hits Out

Lord Justice Leveson condemned the "culture of reckless and outrageous journalism" that dominated sections of the press for decades as he unveiled the findings of his 16-month inquiry on Thursday.

The Appeal Court judge called for a new watchdog with statutory underpinning to be given the power to require prominent apologies and impose fines of as much as £1m.

Mr Cameron immediately voiced "serious concerns and misgivings" about legislative action, and said the press should be given a "limited period of time" to show it could get its own house in order.

Labour leader Ed Miliband said: "Many of the victims of sections of the press will be feeling utterly betrayed by David Cameron."